Abstracts - KTH Mechanics

3D chaotic mixing inside drops driven by transient electric field
Xiumei Xu a and G. M. Homsy a
We study the 3D chaotic trajectories inside a neutrally buoyant drop driven by
periodically switching a uniform electric field through an angle . The extent of the
chaotic mixing is related to two parameters: the angle and modulation period T. In a
static electric field, the streamlines internal to the drop are axisymmetric Taylor
circulations with two rings of center fixed points (CFP) at the top and bottom
hemispheres corresponding to the vortex center. Periodically switching the field is
equivalent to periodically changing the axis of symmetry, and thus the position of
these CFPs. There are always common CFPs during the field rotation, and there are
either 4 or 8 depending on the range of . When equals /2, although the
trajectories are three dimensional, Poincare maps show that for all modulating periods,
the 3D trajectories are confined to certain KAM surfaces, determined only by initial
positions, which limit the mixing. For other than /2, chaotic mixing is generated
inside the drop, but there are ordered regions near the common CFPs, with more
regions for the larger number of common CFPs (Figure 1). Inside the ordered regions,
trajectories move around the common CFPs in complicated way, and the Poincare
maps can exhibit highly ordered fractal structures. The mixing also depends on the
modulating period, and our numerical results show that by modifying T it is possible
to break the ordered islands and achieve global chaotic mixing. These results suggest
there are optimum operating conditions that maximize mixing.
a University of California-Santa Barbara, Santa Barbara, 93106, USA
z
(a) (b)
z
y y
Figure 1: Typical Poincare maps, T=6, (a) =0.45 , the case of 8 common center
fixed points; (b) =0.25 , the case of 4 common center fixed points.
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